I think, in general, the solid body guitar is the most versatile design you could buy. In fact I heard a guy on youtube playing a strat through some fairly large effects box and it sounded very very much like a 6 string acoustic. I was amazed to hear it.
Having said all that the point of this...what would you think I would need to get a stock Fender Stratocaster to sound, if not the same, at least very similar to BB King. If I'd just be wasting time and money just say so, as I am sort of thinking that already but I thought I'd ask.
You could use a Strat to get a very good Blues sound. Blues sounds are easy, though.

You will not get a BB King-like tone from a Strat (BB King was most famous for using a Gibson semi-hollow, a sound the strat struggles to replicate).
Actually, I go by Dave, but there are already too many Daves on this forum.

Fender MIM Stratocaster
Fender Jaguar Bass
Epiphone EJ200 Super Jumbo
Fender Excelsior 13w
Acoustic B300HD (with matching 1x12 cab)
NYC Big Muff Pi
it really depends on how picky you are. while you may not sound dead on like BB a strat can give you some great blues tones. so can a tele, or a flying V for that matter.

how you play can be just as important to what you are playing on.

what amp are you using?
if you are talking a strat with single coils then you are really barking up the wrong tree. BB used (for the most part) a semi-hollow gibson with humbuckers. the guitar also featured a varitone which produces sounds that you aren't likely to get oout of a strat.

a strat of course can provide you with a nice clean tone which of course is what BB used most of the time. i'd suggest that you hook up the middle pickup tone contro to the bridge so you can roll back the treble. i'd also suggest getting a solid state amp that does a really good clean sound. you won't sound exactly like BB but you should be able to get a decent sound for that style.